A Competition Model with Dynamically Allocated Inhibitor Production

The chemostat is a basic model for competition in an open system and a model for the laboratory bioreactor (CSTR). Inhibitors in open systems are studied with a view of detoxification in natural systems and of control in bio-reactors. This study allows the amount of resource devoted to inhibitor production to depend on the state of the system. The feasibility of one dependence is provided by quorum sensing. In contrast to the constant allocation case, a much wider set of outcomes is possible including interior, stable rest points and stable limit cycles. These outcomes are important contrasts to competitive exclusion or bistable attractors that are often the outcomes for competitive systems. The model consists of four non-linear ordinary differential equations and computer software is used for most of the stability calculations.